bekenstein and hawking by introducing temperature and every black hole has entropy and using the first law of thermodynamic for black holes showed that this entropy changes with the event horizon surface. bekenstein and hawking entropy equation is valid for the black holes obeying einstein general relativity theory. however, from one side einstein relativity in some cases fails to explain experimental observations and on the other side, string theory indicates that some corrections should be applied to the hilbert-einstein action. therefore, extended gravity theories were presented. these extended theories may bear black hole solutions. now one may pose a question that how the entropy of such new black holes may be defined. wald applied a symmetric general gravity theory (diffeomorphism) and proposed a method for defining the entropy. in wald’s method, the entropy is proportional to noether charge corresponding to the diffeomorphism symmetry which for hilbert-einstein action is found to be the same entropy of bekenstein -hawking. recently, ashoke sen showed that the wald’s entropy for d-dimensional spherically symmetric extremal black holes which reveal near horizon geometry,may be found in a simpler form. this method also give a better understanding of behavior of scalar fields on the black hole’s horizon. this thesis presents black hole and its thermodynamics and then studies wald’s approach and entropy function .